In many marine operations and studies, it is necessary to have accurate data relative to wave height and frequency. In relatively shallow water such data may be obtained by attaching measuring instruments to fixed structures, such as bridge abutments, piers, piles, etc. Wave measurement in deeper water where no fixed instrument support is available has employed buoys to support the measuring instruments. Two general types of buoys have been employed. The first type is a very long thin spar buoy adapted to float vertically. Such a buoy is relatively stable and provides a good support for measuring instruments. However, such spar buoys are difficult to launch and retrieve due to their great length and small diameter and such launch and retrieve cannot be accomplished from a small boat. The second type of buoy employed is more compact and can be launched and retrieved from a small boat. Such buoys tend to follow the wave surface and are equipped with instruments, such as an accelerometer to measure the vertical movement of the buoy. However, such buoys pitch and roll and this motion results in inaccurate data. Attempts to reduce or eliminate the effect of roll and pitch have been incorporated in some of the prior art wave measuring buoys. U.S. Pat. No. 3,769,838 discloses an electronic circuit intended to remove that energy in an accelerometer signal caused by the tilt of the accelerometer. Many times this will remove real wave data. Another prior art wave measuring buoy has maintained an accelerometer in a vertical position by means of a gyroscope so that it will measure only vertical accleration. This device is effective but is extremely expensive.